Oh, and the 2nd part of the question (what is probability Bears win at least one game), is their odds of winning exactly all four + the odds of winning exactly three + odds of exactly two + odds of exactly one.

Why Would I Read the Article:here N and K are 4, P is .2 and Q is .8, says that the probability of the Bears winning all four games when they have a 20% chance of winning any single game is only .0016%

Why Would I Read the Article:Why Would I Read the Article: here N and K are 4, P is .2 and Q is .8, says that the probability of the Bears winning all four games when they have a 20% chance of winning any single game is only .0016%

I'm an idiot. It's .16%, not .0016%. Math is hard.

Yes you are. And your notation stinks too. You are missing some exponents and your variables change from upper to lower case for no reason.

The problem's unsolvable as written. You can only multiply the probabilities if the results of the individual games are independent of each other, and I see no reason why that assumption is anywhere close to reasonable.

kevinatilusa:The problem's unsolvable as written. You can only multiply the probabilities if the results of the individual games are independent of each other, and I see no reason why that assumption is anywhere close to reasonable.

It seems less reasonable than assuming (taking the classic example) that coin flips are independent. Coins don't get concussions.

However, the problem states clearly that the Packers have an 80% chance each time, and hey, you can only solve the problem you're given.

Why Would I Read the Article:Oh, and the 2nd part of the question (what is probability Bears win at least one game), is their odds of winning exactly all four + the odds of winning exactly three + odds of exactly two + odds of exactly one.

So .0016+ .0256+ .1536 + .4096 = .5904

The other way to think about this problem is that "The bears winning at least one" is the complement of "The bears losing all four." So you can calculate the easier probability that the bears lose all four and subtract from one:

Normally if you go one-on-one with another team you have a fifty-fifty chance of winning. But the Packers are genetic freaks, and they're not normal. You've got a 20%, at best, of beating them. And then you add in referees to the mix, your chances of winning drastically go down. See, the division games, at Lambeau, you have a 33 and 1/3 chance of winning, but I got a 66 and 2/3 chance of winning, cause the Bears know they can't beat them, and they're not even gonna try. So Bears fans, you take your 33 and 1/3 chance, minus the Packers' 20% chance, and you've got an 8 and 1/3 chance of winning at Lambeau. But then you take the Packers' 75% chance of winning, if they were to go one-on-one, and then add 66 and 2/3 percent, the Packers have 141 and 2/3 percent chance of winning at Lambeau. You see Bears, the numbers don't lie.

Players can't afford to hate anyone any more, because with free agency mucking up the teams each year, they may be your team next year.

Great Packers-Bears story. sorta - when George Allen broke his contract as George Halas's defensive coach to become head coach with the Rams, Halas was royally honked off and vented at a league meeting: "Nobody should hire George Allen! Allen is a cheat! Allen is a charlatan! He cannot be trusted!"

At which point Vince Lombardi leaned over to Rams owner Dan Reeves and said "Dan, sounds like you got a helluva coach."

That is the only line in that movie that was nonsense. There is no way a judge that has spent the entire movie preaching rules and decorum would allow that kind of language in his courtroom. Plus, Pecsi's character did such a good job in befriending the jury (such as calling the elderly black lady "dear") that such language would have alienated such a genteel jury.

No. But the Packers fans are pretty goddamn smug for being a bunch of perpetual alcoholics.

We are not smug, just alcoholics. I am not a huge sports fan, but I can say out of the Vikings, Packers, and Bears fans, the Vikings fans are worse. They are really big assholes, and honestly wish players to get hurt. Packers and Bear fans can go either way, they are either really considerate and just love the game of football, and respect other fans or they are just asses.